(Octahedral) holonomy maze
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- Опубликовано: 3 май 2021
- Available from Shapeways: www.shapeways.com/shops/henry...
Thanks to Chaim Goodman-Strauss for the sculpture, to Saul Schleimer for naming the "rook", and to Sabetta Matsumoto for helpful conversations.
Wow this such a cool puzzle idea! For some reason, the mechanism reminds me of a Latch Cube (variant of a Rubik's cube that prevents you from making some particular moves, to make it harder), but I'm honestly not sure how similar they work behind the hood. Both are pretty challenging though, I bet!
I’m pretty sure that holonomy maze is much easier! It has only 24 states. I wasn’t familiar with Latch Cube - I assume that it has a ratchet-like mechanism that clicks as you rotate the faces to prevent backwards motion?
@@henryseg The rachet-like mechanism is in the edge pieces. This cause not just forcing to turn one way, but if two edges have opposite rachet directions on the same face, that face cannot turn. This blockage occurence much more chaotic than the holonomy maze.
no way it's 100% real cary keyhole not clickbait
holy crap its cary kcary hcary
you the guy who created bfdi right?
Very cool puzzles! I'd love to see an even more difficult one with icosahedral lanes rather than octahedral, where holonomy rotates you increments of 2pi/5. Not sure how much that complicates the 'rook' system you're using though... might need another rail due to the odd number of sides.
I've thought quite a lot about an icosahedral version - I don't currently see a way to have the rook be able to move in any of the five possible directions at a vertex but not be able to rotate. (Let me know if you see a way to do it!) However, I do have a design I'm working on for a dodecahedral version - going around a pentagonal face would rotate by 4pi/12 = pi/3. (I think that a triangle of the icosahedron would give holonomy of 4pi/20 = pi/5.)
One could simulate these puzzles using graph theory. The puzzle in the video was a 4-regular graph with 24 vertices. In order to make it a puzzle, several edges are removed. From there the player tries to find a trail leading from the start vertex to the end vertex. Your idea would require a 5-regular graph with 60 vertices. The dodecahedral version would need a 3-regular graph also with 60 vertices. So the puzzle could be made in a simulation worst-case scenario.
It turns out that the dodecahedral and icosahedral versions both have 120 vertices! Work in progress…
@@henryseg Oh, I see my mistake, I was counting vertices by V*d where V is the shape's number of vertices and d is the degree of each of the shape's vertices. I should've done V*n where n is the smallest natural number which satisfies (2*n/f=int) where f is the number of faces.
@@henryseg Here's a structure that works for the dual dodecahedral one. The black dots are rigidly connected and slide on 3 rails. It can translate but not rotate. The same trick works for icosohedral vertices, but then you need 5 rails and that gets annoying. Sorry for the crappy MS paint drawing lol: ibb.co/bvkQ6jg
This is what advanced alien races give to their babies as toys and I'm absolutely here for it
This is my new favorite way to learn new words
I'm not a puzzle person but by golly the aesthetic of these puzzles looks gorgeous and I would love to buy a bunch of different colours to keep them as ornamental pieces around the home that have the bonus of people being able to interact with.
Have a holly jolly Christmas
Exceptionally interesting and clever, even by your standards. Now I must look up the Gauss-Bonnet theorem.
This is such an artifact level puzzle that it would make a bomb D&D puzzle prop
Like, if you replaced the "rook"'s boxes with the figure of a dual-wielding warrior? Yaas
@@danieltaber4924 I was thinking just LED glowing orb honestly, but that sounds pretty neat as well
@@Owen-bk5fc Ooh, combine the two, so that the track is glowing and the rails resemble stone or metal?
Ooh, you could even have the swords have different properties, like height v length, so that the Gates can be made to block one, the other, or both!
I thought about making a maze with that kind of control - you could individually block or allow any of the paths in the graph, and presumably make a longer or loopier maze. I liked the simplicity of the arms and pegs all being on the same level for this version.
The Sculpture looks like the Cayley Graph of a Group.
I really must get a set to experiment with these mazes in Group theory!
That's just beautiful. Great visualization of the state transitions too...
Can these mazes always be solved by using the “right hand rule”? I think a maze could be designed that would return the rook to the start, un-rotated, if all right branches are taken, but in that case I think that taking all left branches will lead to a solution, so still yields to the rule. But I’m having trouble visualizing how the pegs block some rook rotations and pass others, so I think I need to hold an actual example in my hand 😀
For mazes without weird rotation stuff, the right hand rule may fail if there are loops. That’s also true here, and the loops can get pretty complicated, so my guess is that this doesn’t work in general.
I found the most underrated channel in youtube and its gold.
Henry, my friend, you never cease to amaze!
Damn! What a great way to intuit holonomy. Fantastic
Very interesting, informative and worthwhile video.
I've seen these on Mr. Puzzle! I didn't realize you are the designer, very cool!!
Beautiful work.
Very reminiscent of some of Oskar van Deventer's maze-type puzzles
Many thanks, very good explanation
🤯 absolutely wonderful!
really nice e very well explained!!! thank you.
So awesome!
I think you’ve got a real winner with this one. 👍
How cool is that!
The routes here are basically following the edges of an octahedron. Could you make one that follows the edges of a cuboctahedron or an icosidodecahedron?
I have a dodecahedral version planned… with other shapes I think you get into trouble - the geometry at the intersections of the paths would have to be slightly asymmetric, which would be trouble when the rook gets back to it rotated.
One of these should come with the definition of holonomy in a differential geometry book
Excellent! I just bought both mazes for use in my differential geometry lectures.
Thanks!
@@henryseg Keep up the great work!
Why is a system with the property of a path-dependent state called 'Nonholonomic' on Wikipedia? Do physics and mathematics have opposite terminologies?
Howwww did I miss this video? It's so good
I love this!
That's frikkin awesome
amazing print!!
Smart... amazing actually...smart choice of colors
This is so cool omg
Nice one!
Mr. Puzzle would love this
this is really cool actually
I like this puzzle.
What a video!
Would it be possible to buy the stl files to print at home?
Is there a 3D model for this? I would love to 3D print it
I can't believe they made Devil fruits that work as a puzzle
Waw. Well explained
very cool
I love how my brain didn't understood half of the things that happened here
That is absolutely mind boggling, I got completely lost at the sentence at 4:03, what does "taking a ball and glueing opposite points on it's boundary" mean?
It seems rather intuitive to mess around with, but the understanding behind it is another ball game completely. Also how do you get the rook in the starting position if they get printed separately?
I want a 3d printer now(I don't got the money nor the space tho haha), just so I can try and solve it haha, I'd also like to learn to make them and different iterations and see how hard they can get. Thank you for uploading!
the rook is able to be removed or replaced when it is in the correct orientation in the start area, and then you move it around so its back in the start position with a different rotation.
this looks like a really cool idea for a puzzle for the hanayama series
Might be a bit big for their standard boxes?
@@henryseg i could see it being made into a puzzle similar in size to cast twist? sounds plausible to me
Yaw pitch roll < quaternions
So cool
Woww, Virologietraining!
My mind while watching this: *"Wolfhook berries..."*
This could be a neat 3d printing project
Was expecting Sethbling outro music at the end there, idk why lol
This kind of reminds me of the brain teaser on changing your hand facing palm up to palm down without twisting/moving your wrist.
First thing that came to my mind when I saw it was the gomu gomu no mi
the puzzle looks like the core of a 2x2 rubik's cube.
Thats cool
looks like a grape !!!!! new sub
Is it possible to make a version of this were you can change the location of the pins in the sphere, made in such a way you can never make it impossible? That way you could make a randomizable puzzle that is different to solve every time like a twisty puzzle.
Really cool puzzle!! I wish I could afford one! I have too much student loan debt at the moment.
Have you ever thought about designing a chess-like game? I wanted to make one with different verticies or tile axises like hexagonally tiled plane 2-6 player or like Robert Penrose tiles with 2-5 players. Lmk if you think it's worth the energy!? I've made a few turn based card games with dice and prototype cost is a lot higher than one would think.
nice
Is there a way I could get the file to 3D print it ?
Cool idea and design. But do you win if this is a puzzle?
what if each vertex had a different amount of tiles??
This is excellent. I missed if you said the paths were the longest possible or just any that connected the points for enter and exit.
There are slightly longer mazes, but the longer examples are more like trees, with no loops. So, not as fun to play with, and probably also easier to solve.
@@henryseg awesome!
@@henryseg Interesting to see game design come into this. It's cool to think about what constitutes a "fun" maze
Yes, you think you're doing math and engineering, and suddenly you're in psychology land!
@@henryseg did you put the full list of maze paths anywhere online?
Ah yes, triangles made up of 3, 90° angles. I love non-euclidean geometry
Do you have this maze toy with removable pegs? To make mazes on the fly?
this is a shift gear for nasa's origami robots
Is there anywhere I can just buy an STL of this?
I think someone is a secret Evangelion fan.
A puzzle based on Group Theory
i mean yeah rotation is 3d that's why most programmes also use a vector3 for rotation as well as position
What is it called when you do it with your elbow?
dude, patent this. cuz one of the days one guy is gonnamake 3d-maze puzzles and take all the stuff you did and get rich over it!
Maybe make easier or harder versions? For example maybe the easy version has a 1 armed rook? And maybe the harder version has 3 arms?
Is the visualization available somewhere?
Was going to buy one but rook sold seperately.
It's a necessary side effect of the way that Shapeways has their service set up. If I included the rook in with the maze then it wouldn't be possible to have it in a different colour.
do you sell files for 3d printing too?
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hi there, pretty cool video, i love to see the mathematical explanation behind the puzle, i took a look at your shop and to be honest, they are way more expensive than i spected since they are (i think) 3D printed, don´t get me wrong, i´m sure they are worth the prize, but i´m curious about why do some of the things in the store cost that much (for example the 24-cell Monkeys), i guess that it´s because of the research and work it takes to make the pieze, or maybe the material it´s made from, but 2k for sure is a lot of money, and i´d love to hear the reason behind it.
thanks again for such a cool video, have a nice day
Almost everything in my shop has a 35% markup over the price that Shapeways charges. So, I'm not getting that much from them. I mostly use Shapeways' SLS nylon material, which is much higher quality than desktop FFF 3D printing, but is unfortunately quite a bit more expensive.
Where can i buy this?
😂when I saw the preview, I thought it was a model of COVID-19 virus
What was used for the animations? And graphs?
Grasshopper, the visual programming language in Rhino3D.
@@henryseg never heard of it, thanks!
So hat happens if you rotate around the first triangle shown more than once? You end up solving the puzzle without traveling anywhere else.
The pegs block that move.
Is it just me, or does anyone else thinks it kinda looks like the gomu-gomu no mi?
Shut up and take my money! I wanna figure out the math myself!
Its like touching a PARENT'S "SECRET",.... which means getting g BUSTED was SOOOOOOO "WORTH IT"😁
Cuz. Like....not "ANYONE" had BEEN "THERE"❤
Holo Holo no Mi Devilfruit
GOMU GOMU NOOOOOOO
You could probably sell some of the things that you've made
I'd buy some thing
I do sell them at www.shapeways.com/shops/henryseg. Unfortunately, high quality 3D printing is very expensive in comparison to injection molded plastic.
Make these pins(they stop rook) changeable
It’s a good idea, but it’s not easy to engineer removable pins that don’t wobble or come out accidentally, and it’s even harder if you want the pegs to be small like they are in these mazes.
Bruh why are you not selling these
See the description of the video!
This is a cool cool video dawg, but y'all need some music or an intro or something
Looks like the old playstation network logo
The math behind it is also similar to the logic to relativity is you think about it to solve it
shinji's mom
"zee"?!
Am I the only one who got reminded of a devil fruit?
𝙏𝙃𝙀 𝙀𝙂𝙂𝙋𝙇𝘼𝙉𝙏𝘽𝙀𝙍𝙍𝙔
Hmm
this looks like the playstation network logo
at first I though the sculpture looked like a finite projective plane, but then I saw that similar colored lines dont intersect at all, so it isnt.
Sad Jenaf sad bcasue I like projective geometries.
or is it a finite projective space and I was just too used to the plane version? the way the ball surface used for the orientation space are glued back together..
yay it is, Jenaf happy again.